{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Calculation\n",
    "\n",
    "Determining the gradient of an arbitrary loss function, e.g., RMS spot size or Strehl ratio, with respect to lens parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import optiland.backend as be\n",
    "from optiland.samples.objectives import ReverseTelephoto\n",
    "from optiland.analysis import SpotDiagram\n",
    "from optiland.psf import FFTPSF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "be.set_backend(\"torch\")  # all calculations will be done using torch\n",
    "be.set_precision(\"float32\")  # or \"float64\" for double precision\n",
    "be.grad_mode.enable()  # enable gradient calculation. Can also be set to \"disable\" to save memory if gradients are not needed.\n",
    "be.set_device(\"cuda\")  # run on GPU if available, otherwise use \"cpu\" option"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "lens = ReverseTelephoto()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spot = SpotDiagram(lens)\n",
    "spot.view()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Record the lens radii of curvature as parameters\n",
    "radius_params = []\n",
    "surf_idx = []\n",
    "for idx, surf in enumerate(lens.surface_group.surfaces):\n",
    "    if not be.isinf(surf.geometry.radius):  # only add non-infinite radii\n",
    "        # Create a new tensor for the radius with gradient tracking enabled\n",
    "        r = (\n",
    "            surf.geometry.radius.clone()\n",
    "            .detach()\n",
    "            .requires_grad_(True)\n",
    "            .to(be.get_device())\n",
    "        )\n",
    "        surf.geometry.radius = r\n",
    "        radius_params.append(r)\n",
    "        surf_idx.append(idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We decide to build a dual loss function consisting of:\n",
    "\n",
    "1. The RMS spot spot size at (Hx, Hy) = (0, 1) field and 0.5876 µm.\n",
    "2. The Strehl ratio for the on-axis field.\n",
    "\n",
    "Any combination of analyses or calculations can be included in the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. Compute the RMS spot radius\n",
    "spot = SpotDiagram(lens)\n",
    "field_idx = 2\n",
    "wave_idx = 0\n",
    "rms = spot.rms_spot_radius()[field_idx][wave_idx]\n",
    "\n",
    "# 2. Compute the Strehl ratio\n",
    "psf = FFTPSF(lens, field=(0, 0), wavelength=0.5876)\n",
    "strehl = psf.strehl_ratio()\n",
    "\n",
    "# 3. Compute the joint loss function & backpropagate\n",
    "loss = rms + strehl\n",
    "loss.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute gradients\n",
    "gradients = [r.grad.item() for r in radius_params]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the gradients\n",
    "plt.figure(figsize=(10, 5))\n",
    "\n",
    "gradients = np.array(gradients)\n",
    "normalized_heights = (gradients - gradients.min()) / (gradients.max() - gradients.min())\n",
    "cmap = plt.get_cmap(\"coolwarm\")\n",
    "colors = cmap(normalized_heights)\n",
    "\n",
    "plt.bar(\n",
    "    range(len(gradients)),\n",
    "    gradients,\n",
    "    color=colors,\n",
    "    tick_label=[f\"Surf {i}\" for i in surf_idx],\n",
    ")\n",
    "plt.xlabel(\"Surface Index\", labelpad=10)\n",
    "plt.ylabel(\"Gradient Magnitude\", labelpad=10)\n",
    "plt.grid(alpha=0.25)\n",
    "plt.axhline(0, color=\"black\", lw=0.5, ls=\"--\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
